Unfortunately, because there can be dozens or even hundreds of disease-causing mutations in every dog, there will always be another genetic problem waiting in the wings to suddenly pop up in a breed. If we had tests for all the mutations found in purebred dogs, both the ones we know about and the ones that have not yet been identified, it would become impossible to breed if breeders wanted to avoid every risk.
You can appreciate the futility of this search-and-destroy strategy when you see that even now, the number of known disorders in dogs outstrips the available tests. This is genetic whack-a-mole, and it will be no more successful in eliminating genetic disorders in dogs than the strategy of trying to rid your yard of moles by shooting just the ones that stick their heads out of a hole.
Smaller populations become inbred more quickly, so the simplest way to reduce the rate that inbreeding is to maintain a larger population of breeding animals. The easiest way to do this without producing an oversupply of puppies is to increase the number of different sires being used in breeding. Instead of a few individuals producing most of the next generation, limit the number of breedings per individual and make use of more dogs.
Popular sires are a double whammy on the gene pool. Not only do they reduce the number of male dogs contributing to the next generation by doing more than their fair share of breeding (see #1 above), they also distribute dozens or even hundreds of copies of their mutations (and ALL dogs have mutations!) in the puppies that they produce. The pups might all be healthy because they got only one copy of a mutation, but a generation or two down the road, those mutations will start showing up in pairs and suddenly breeders will find themselves dealing with a new genetic disease that seemingly came out of nowhere. In fact, the new genetic problem is the completely predictable result of a breeding strategy that creates many copies of a particular dog's mutations. Blaming the dog ("We didn't have this awful problem until Fido introduced it to the breed!") is only an effort to deflect responsibility, because every breeder that used him as a sire participated in creating the resulting genetic problem. (For more about this, read The pox of popular sires.)
In many breeds, there are genetically-distinct subpopulations of dogs. They might represent bench versus field lines, color or coat varieties, geographic areas, size, or some other factor. Because they carry genes that will be less common in other groups, they can be used to reduce the level of inbreeding in a litter of puppies. The number of loci that are homozygous (with two copies of the same allele) will be reduced, and therefore the risk of expressing a recessive mutation will be less. An outcross every now and then can be sufficient to reset the inbreeding to a healthier level.
By the way, you will hear some breeders claim that outcrossing will introduce new genetic disorders to your dogs. But if you understand how recessive genes work and you practice good genetic management, those new mutations are no different than the ones already in your lines - they won't cause any problems unless you create puppies that inherit two copies in the same one. New mutations will have low frequencies in the population, and sound genetic management will keep it that way. (See Using inbreeding to manage inbreeding.)
Every dog - in fact, every animal - has mutations that could potentially cause disease, and don't let anybody try to claim that their dogs are any different. The key to producing healthier dogs is breeding in a way that reduces the chance that an animal will inherit two copies of the same mutation. Doing the available DNA tests for a breed then producing a litter with an inbreeding coefficient of 20% is self-defeating and just asking for trouble.
Money to identify mutations, develop tests, and screen potential breeding stock is all for naught if we are using breeding strategies that are specifically designed to increase homozygosity of the genes for desirable traits, because homozygosity of mutations will necessarily increase as well. You cannot do one without the other.
If we're serious about reducing genetic disorders in dogs, the things we must do are simple and clear. It is responsible breeders, not researchers and DNA tests, that will reduce the burden of genetic disease in dogs.
You can learn more about the basics of sound genetic management of breeds and populations in the courses offered by the Institute of Canine Biology. The next course, Managing Genetics for the Future, starts Monday, 1 February.
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